Multiply Conjugates Using the Product of Conjugates Pattern
In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern
323. (c − 5)(c + 5)

Answer:

A ≈ 1194.5

The total surface area is 1194.53.

a = 24

b = 30

c = 7

h = 18

Answer:

C. 92.16π mi²

Step-by-step explanation:

Use the formula: 4 · π · r²

r=4.8

4 · π · 4.8²=

=4 · π · 23.04=

=92.16π mi²

Hope this helps!

If not, I am sorry.

Answer:

v = 2u

Step-by-step explanation:

note that

2u = 2 (5, - 2 ) ← multiply each component by 2

    = (10, - 4) = v , then

v = 2u

yd=

yd=

16x2+12x+18=3x=2x2+6x+9=3x=

sorry i try

Answer:

D

Step-by-step explanation:

By the converse of the basic proportionality theorem, we can say DE║AB.

We need to check whether DE is parallel to AB.

If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

In triangle ABC, we can see on side AC, D is midpoint (∵AD=DC) and on side BC, E is midpoint (∵BE=CE).

Therefore, by the converse of the basic proportionality theorem, we can say DE║AB.

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The proof is shown below:

The line segment joining the mid points of any two sides of a triangle is parallel to the third side.

△ABC in which D and E are the mid points of AB and AC,.

If D and E are the mid points of AB and AC,

then AD=DB and AE=EC.

Thus,

AD/DB = AE/ EC

​

by the converse of Thales theorem, DE∥BC.

As, by theorem we can say that DE∥BC.

So, there is no other side parallel to DE.

​

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Answer:

9x - 2

Step-by-step explanation:

f(x) = 4x - 8

g(x) = 5x + 6

because it's (f + g)(x), we can simply add the functions together

{note: don't get thrown off by the (x) being separate parentheses--distributing the x first can help it look familiar:

(x)(f + g)

fx + gx,

it's the same thing}

(4x - 8) + (5x + 6)

here, we want to combine like terms to simplify:

4x + 5x - 8 + 6

4x + 5x  -   2

9x - 2

So, (f + g)(x) = 9x - 2

hope this helps!! have a lovely day :)

Answer:

2700 - 2000 = 700 - 100 = 600 - 200 = 400 - 100 = 300

300 dollars

Answer:

c. x=8

Step-by-step explanation:

make me a brain list.

The probability of both events occurring is  4/15

The given parameters are:

P(A) = 4/5

P(B) = 1/3

Because the events are independent, we have:

p(A and B) = P(A) * P(B)

This gives

P(A and B) = 4/5 * 1/3

Evaluate

P(A and B) = 4/15

Hence, the probability of both events occurring is  4/15

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Answer:

4.09 seconds

Step-by-step explanation:

simplify miles per hour to feet per second how many feet is a mile and how many seconds are in an hour you end up with 88 fps from 60 mph

now simply a football field is 360 feet so 360/88 is 4.09090909 etc

Your eyes off the road for 4.09 seconds.

The rate of change of position of an object in any direction is called the speed.

Given that, Taking your eyes off the road for how many seconds at 60 miles per hour means you have travelled blindly for half the length of a football field,

Converting 60 mph into fps

60 mph = 88 fps

The length of a football field = 360 ft

Time = 350/88

= 4.09 seconds.

Hence, you travelled for 4.09 seconds.

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The answer choice which represents a solution to the system of equations is; (–2, 10).

The system of equations as given in the task content is;

-6x - (2/5)y = 8

(1/2)x +3y = 29

Hence, by making x subject in equation 1 and substitution; we have;

x = (-0.4y -8)/6

Hence; (0.4y -8)/12 + 3y = 29.

(0.4y -8) + 36y = 348

35.6y = 356

y = 10

and x = (-0.4(10) -8)/6 = -2.

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Answer: 28.40 cans of soda

Step-by-step explanation:

Volume of cylinder: pi * r^2 * h

Volume of the can of soda = pi * 3.25^2 * 12 = 126.75 pi

Volume of the cylindrical pitcher = pi * 10^2 * 36 = 3600 pi

3600/126.75: 28.40 cans of soda

Answer:

28 whole soda cans or 28.4 soda cans (rounding to nearest tenth)

Step-by-step explanation:

The soda cans and the pitcher can be modeled as cylinders.

Volume of a cylinder

  [tex]\sf Volume=\pi r^2h[/tex]

where:

Diameter of circle

[tex]\sf d= 2r[/tex]

[tex]\sf \implies r=\dfrac{1}{2}d[/tex]

Volume of Soda can

Given values:

[tex]\begin{aligned}\sf \implies Volume & = \sf \pi (3.25)^2 \cdot 12\\ & = \sf 126.75 \pi \:\:cm^3\end{aligned}[/tex]

Volume of Pitcher

Given values:

[tex]\begin{aligned}\sf \implies Volume & = \sf \pi (10)^2 \cdot 36\\ & = \sf 3600 \pi \:\:cm^3\end{aligned}[/tex]

To calculate how many cans of soda the pitcher will hold, divide the volume of the pitcher by the volume of one soda can:

[tex]\begin{aligned}\implies \textsf{Number of soda cans} & = \dfrac{\textsf{Volume of Pitcher}}{\textsf{Volume of one soda can}}\\\\&= \sf\dfrac{3600 \pi}{126.75 \pi}\\\\& = \sf 28.402366...\end{aligned}[/tex]

Therefore, the pitcher can hold 28 soda cans (nearest whole can), or 28.4 soda cans (nearest tenth).

The different sets of initials can be formed if every person has one surname (i.e., last name) and either one or two given names (i.e., a first name, or a first and middle name) is 15600.

There are 26 possible letters, each set of initials would have 3 letters in it, order doesn't matter, i.e. ABC does not equal ACB. using permutation   26P3 = 5600.

A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters. Common mathematical problems involve choosing only several items from a set of items in a certain order.

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Rachel should perform better because of the spacing effect.

Given,

Rachel will study one hour each day for 5 days and Jennifer will study 5 hours the day before the exam.

What do you predict about their scores?  

Rachel should perform better because of the spacing effect.

The spacing effect demonstrates that learning is more effective when study sessions are spaced out. This effect shows that more information is encoded into long-term memory by spaced study sessions, also known as spaced repetition or spaced presentation, than by massed presentation.

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The equation of the line passing through the points is y = x + 2

The points are (-1, 1) and (4, 6).

The slope is calculated using:

m= (y2 - y1)/(x2 - x1)

So, we have:

m = (6 - 1)/(4 + 1)

Evaluate

m = 1

The equation of the line is then calculated as:

y = m(x -x1) + y1

This gives

y = 1 *(x + 1)  + 1

Evaluate

y = x + 2

Hence, the equation of the line passing through the points is y = x + 2

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The Area of triangle is A= 58.02 (ft)^2

According to statement

Let

B is the measure of the vertex angle of the isosceles triangle ABC

A and C is the two congruent sides of the isosceles triangle ABC

we know that

The area of a triangle applying the law of sines is equal to the

A= 1/2 *AC *SinB

we have

A=C= 17.91 ft

And

B= 21.21

Substitute these values in the formula

A= 1/2* 17.91* 17.91 * Sin(21.21)

A= 58.02 (ft)^2

So, the Area of triangle is A= 58.02 (ft)^2

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Answer:

1066

Step-by-step explanation:

5 mins = 410 words

410/5 = 82 so she is typing 82 words a minute

Then do 82 times 13

The value of m is 14.5 and the three angles of the triangle are 32.5°, 57°, and 90.5°.

There are three angles in a triangle. Consider as ∠A, ∠B, and ∠C.

The sum of all the three angles gives 180° in a triangle. I.e.,

∠A + ∠B + ∠C = 180°.

The given triangle has three angles,

(m + 18)° , (2m + 28)°, and (3m + 47)°

On adding all these and equating to 180°,

(m + 18)° + (2m + 28)° + (3m + 47)° = 180°

⇒ 6m + 93 = 180

⇒ 6m = 180 - 93

⇒ 6m = 87

∴ m = 14.5

Then, the values of the three angles are:

(m + 18)° = (14.5 + 18)° = 32.5°

(2m + 28)° = (2 × 14.5 + 28)° = 57°

(3m + 47)° = (3 × 14.5 + 47)° = 90.5°

Therefore, the angles of the given triangle are 32.5°, 57°, and 90.5°.

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7

Step-by-step explanation:

p = 1, q = 72 =49, q = 7

ookrndodnepwkpqq

[tex]\huge\textbf{Hey there!}[/tex]

[tex]\mathbf{-3pq^2 + q^3}[/tex]

[tex]\mathbf{= -3(2.9)(-1.3)^2 + (-1.3)^3}[/tex]

[tex]\mathbf{= -3(2.9)(-1.3)^2 - 1.3^3}[/tex]

[tex]\mathbf{= -8.7(-1.3)^2 - 1.3^3}[/tex]

[tex]\mathbf{= -8.7(1.69) - 2.197}[/tex]

=[tex]\mathbf{ -14.703 -2.197}[/tex]

[tex]\mathbf{= -16.9}[/tex]

[tex]\huge\textbf{Thus, your answer should be: \boxed{\mathsf{-16.9}}}}\huge\checkmark[/tex]

[tex]\huge\textbf{Good luck on your assignment \& enjoy}\\\huge\textbf{your day!}[/tex]

The number of people coming in during the lunch hour is 160

The complete question is in the attached image

The random numbers are given as:

18, 38, 87, 16, 56, and 5

Regroup the numbers

Number           Group       Probability

5, 16, 18           1 - 20             3/6

38, 56             21 - 60           2/6

56                    61 - 90          1/6

Based on the individual numbers and the probability table, we have:

X      20      30     40

P     3/6     2/6    1/6

The expected value is:

[tex]E(x) = \sum xp[/tex]

This gives

E(x) = 20 * 3/6 + 30 * 2/6 * 40 * 1/6

Evaluate

E(x) = 160/6

There are six ten-minute intervals.

So, we have:

People = 6 * 160/6

Evaluate

People = 160

Hence, the number of people coming in during the lunch hour is 160

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The ordered pair that is on g(x) is (2, -3/400)

determine the ordered pair:

The function is given as:

f(x)=3/4(10)∧-x

The rule of reflection across the x-axis is:

g(x) = -f(x)

So, we have:

g(x) = -3/4(10)∧-x

Set x = 2.

So, we have:

g(2) = -3/4(10)∧-2

Evaluate the exponent

g(2) = -3/4 * 1/100

Evaluate the product

g(2) = -3/400

This means that:

(x, y) = (2, -3/400)

Hence, the ordered pair that is on g(x) is (2, -3/400)

Ordered pairs are pairs of two numbers (or variables) that are enclosed in parentheses and separated by commas. For example, (1, 2) is an ordered pair. Coordinate geometry represents points, and set theory represents elements of relations / Cartesian products.

Ordered pairs are pairs of numbers in a particular order. For example, (1, 2) and (-4, 12) are ordered pairs. The order of the two numbers is important. (1, 2) is not equivalent to (2, 1)-(1, 2) ≠ (2, 1).

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Multiplying the binomials, we have (x - 7)(x - 2) = x² - 9x + 14.

Applying the distribution property of multiplication, the given binomials, (x - 7)(x - 2) can be multiplied as shown below:

(x - 7)(x - 2)

x(x - 2) -7(x - 2)

x² - 2x - 7x + 14

x² - 9x + 14

Therefore, (x - 7)(x - 2) = x² - 9x + 14.

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Answer:

Hence the expression [tex]$$(x-7)(x-2)=x^2-9x-14$$[/tex]

Step-by-step explanation:

The given expression is (x-7)(x-2).

We have to multiply the given expression.

Multiply the (x-7) by-2, multiply the (x-7) by x then add like terms.

[tex]$$\frac{\begin{matrix}{} & {} & x & - & 7 \\ \times & {} & x & - & 2 \\ \end{matrix}}[/tex]

____________

[tex]{\frac{\begin{matrix}{} & - & 2x & - & 14 \\ {{x}^2} & - & 7x & {} & {} \\ \end{matrix}}{\begin{matrix}{{x}^2} & - & 9x & - & 14 \\ \end{matrix}}}$$[/tex]

The trigonometric function gives the ratio of different sides of a right-angle triangle. The given problems can be solved as given below.

The trigonometric function gives the ratio of different sides of a right-angle triangle.

[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\[/tex]

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

1st.) x = 5 /Sin(30°)

x = 10

!) sin(45°) = 4/x

x = 4/sin(45°)

x = 4√2

I) Cos(45°) = √3 / x

x = √3 / Cos(45°)

x = √6

E) Tan(60°) = 3√3 / x

x = 3√3 / 3

W) For isosceles right-triangle, the angle made by the legs and the hypotenuse is always 45°.

x = 45°

N) x² + x² = (7√2)²

x = 7

V) Tan(60°) = 7 / x

x = 7√3/3

K) x² + x² = (9)²

x = 9/√2

Y) Sin(60°) = 7√3/x

x = 14

M) Sin(30°) = x/11

x = 11/2

T) Sin(45°) = x/√10

x = √5

A) x + 2x + 90° = 180°

x = 30°

O) Sin(45°) = √2 / x

x = 2

R) Tan(30°) = x / 4

x = 4/√3 = 4√3 / 3

S) Sin(60°) = x / (10/3)

x = 5√3 / 3

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Recall the Pythagorean identity.

[tex]\sin^2(x) + \cos^2(x) = 1 \implies \left\langle \begin{matrix} \tan^2(x) + 1 = \sec^2(x) \\ 1 + \cot^2(x) = \csc^2(x) \end{matrix} \right.[/tex]

[tex]\implies \sec^2(\beta) - \csc^2(\beta) = (\tan^2(\beta) + 1) - (1 + \cot^2(\beta)) \\\\ ~~~~~~~~= \tan^2(\beta) - \cot^2(\beta)[/tex]

Recall the difference of squares identity.

[tex]a^2 - b^2 = (a - b) (a + b)[/tex]

[tex]\implies \sec^2(\beta) - \csc^2(\beta) = (\tan(\beta) - \cot(\beta)) (\tan(\beta) + \cot(\beta))[/tex]

[tex]sec^2\beta -csc^2\beta \\(1+tan^2\beta )-(1+cot^2\beta )\\1+tan^2\beta -1-cot^2\beta \\tan^2\beta -cot^2\beta \\(tan\beta -cot\beta )(tan\beta +cot\beta )[/tex]

Using it's concept, it is found that the percentage of the students that do NOT like to travel out of state that like camping is:

B. 34%.

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

[tex]P = \frac{a}{b} \times 100\%[/tex]

In this problem, there are 112 students that do not like traveling out of the state, and of those, 38 like camping, hence the percentage is:

[tex]P = \frac{38}{112} \times 100\% = 34\%[/tex]

Hence option B is correct.

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The correct definition of dependent events is two events are dependent if the outcome of the first event affects the outcome of the second event.

Two events are dependent if the outcome of one of the event depends on the outcome of the first event.  An example of a dependent event is if it rains, the floor would be wet.

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Answer: The three triangles shown are similar triangles. We can tell this by the Angle Angle theory. You can tell the angles are congruent by the matching marks in each corner of the triangles, the marks or “ticks” are the same in the same corners. The length of the sides can change but the angle measurements will still be the same.

Step-by-step explanation: explained in answer

Answer: Each of the corresponding angles of one triangle equal the corresponding angles of the other triangle.

The inverse of the matrix  [tex]\left[\begin{array}{cc}11&-5\\3&-1\end{array}\right][/tex] is the matrix [tex]\left[\begin{array}{cc}\frac{-1}{4} &\frac{5}{4} \\\\\frac{-3}{4} &\frac{11}{4} \end{array}\right][/tex] .

The inverse of a matrix A is calculated by the formula:

A' = (1/|A|)(Adj A),

where A' represents the inverse of matrix A,

|A| represents the determinant value of matrix A, and

Adj A represents the Adjoin matrix of matrix A.

So, to calculate the inverse of the matrix  [tex]\left[\begin{array}{cc}11&-5\\3&-1\end{array}\right][/tex] , we will first calculate its Adj.

Adj = [tex]\left[\begin{array}{cc}-1&-3\\5&11\end{array}\right] ^{T}[/tex]= [tex]\left[\begin{array}{cc}-1&5\\-3&11\end{array}\right][/tex].

Now, we calculate |A| = 11*(-1) - (-5)*3 = -11 + 15 = 4.

Therefore A' = (1/|A|)(Adj A),

or, A' = [tex](1/4)*\left[\begin{array}{cc}-1&5\\-3&11\end{array}\right][/tex] ,

or, A' = [tex]\left[\begin{array}{cc}\frac{-1}{4} &\frac{5}{4} \\\\\frac{-3}{4} &\frac{11}{4} \end{array}\right][/tex] .

Therefore, the inverse of the matrix  [tex]\left[\begin{array}{cc}11&-5\\3&-1\end{array}\right][/tex] is the matrix [tex]\left[\begin{array}{cc}\frac{-1}{4} &\frac{5}{4} \\\\\frac{-3}{4} &\frac{11}{4} \end{array}\right][/tex] .

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